1. Field of the Invention
The invention is related to the field of electromagnetic induction well logging for determining the resistivity of earth formations penetrated by wellbores. More specifically, the invention is related to methods for determining the most likely values of resistivity of the earth formations when the formations have highly conductive layers proximal to low conductivity layers.
2. Description of the Related Art
Electromagnetic induction resistivity instruments are used to determine the electrical conductivity of earth formations surrounding a wellbore drilled through these formations. An electromagnetic induction well logging instrument is described, for example, in U.S. Pat. No. 5,452,761 issued to Beard et al. The instrument described in the Beard et al '761 patent includes a transmitter coil and a plurality of receiver coils positioned at axially spaced apart locations along the instrument housing. An alternating current is passed through the transmitter coil. Voltages which are induced in the receiver coils as a result of alternating magnetic fields induced in the earth formations are then measured. The magnitude of certain phase components of the induced receiver voltages are related to the conductivity of the media surrounding the instrument.
As is well known in the art, the magnitude of the signals induced in the receiver coils is related not only to the conductivity of the surrounding media (earth formations) but also to the frequency of the alternating current. At higher alternating current frequencies, the signals induced in the receiver coils are generally smaller than the signals which are induced at lower frequencies because of the so-called "skin effect". Worse still, the magnitude of the skin effect is also related to the conductivity itself at any particular frequency. While it would appear that merely reducing the frequency of the alternating current would reduce the skin effect in the resulting measurements, it is also known in the art that the magnitude of the induced signals in the receiver coils is proportional to the frequency of the alternating current. Using higher frequencies is desirable in order to enhance the accuracy with which the conductivity can be determined which the conductivity is small.
An advantageous feature of the instrument described in the Beard et al '761 patent is that the alternating current flowing through the transmitter coil includes a plurality of different component frequencies. Having a plurality of different component frequencies in the alternating current makes possible more accurate determination of the apparent conductivity of the media surrounding the instrument by using various methods of estimating the induced signal magnitude that would be obtained in the various receiver coils if the frequency of the alternating current were zero.
One method for estimating the magnitude of signals that would obtain at zero frequency is described, for example, in U.S. patent application Ser. No. 08/608,731 filed by Beard et al on Feb. 29, 1996, now U.S. Pat. No. 5,666,057, and entitled, "Method for Skin Effect Correction and Data Quality Verification for a Multi-Frequency Induction Well Logging Instrument". The method in U.S. Pat. No. 5,666,057 in particular, and other methods for skin effect correction in general, are designed only to determine skin effect corrected signal magnitudes, where the induction logging instrument is fixed at a single position within the earth formations. A resulting drawback to the known methods for skin effect correction of induction logs is that they do not fully account for the skin effect on the induction receiver response within earth formations including layers having high contrast in the electrical conductivity from one layer to the next. If the skin effect is not accurately determined, then the induction receiver responses cannot be properly adjusted for skin effect, and as a result, the conductivity (resistivity) of the earth formations will not be precisely determined.